The Magpies looked set to be heading second in Group F going into their last fixture after Alexander Isak broke the deadlock in the 24th minute.
But PSG scored in the seventh minute of added time after Tino Livramento was somehow adjudged to have handled the ball.
Referee Szymon Marciniak initially waved away the protests, before VAR instructed him to view the incident on the pitchside monitor.
Replays showed he had handled the ball, but only after Ousmane Dembele's cross hit his chest first.
The match official then pointed to the spot, with Mbappe's goal keeping them second in the group - a place and two points above Newcastle.
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Newcastle players were furious with the decision as they protested the decision to Marciniak following the full-time whistle.
Meanwhile club legend Alan Sheaer posted on X: "Do me a f****** favour man. What a load of s***."
Speaking to TNT Sports immediately after the match, goalscorer Isak said: "My first reaction that it wasn't but I haven't seen it back.
"Hopefully, if the penalty was given then it should have been. We have to trust the refs."
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The result means that Newcastle have to beat AC Milan in their final group game in Tyneside and hope PSG fail to beat Borussia Dortmund to stand any hope of advancing into the last-16.